Question

Show that (x – y) is a factor of the polynomial x

3 – 2x2y – 5xy2 + 6y3

Answer 1

Step-by-step explanation:

$p(x) = {x}^{3} - 2 {x}^{2} y - 5x {y}^{2} + 6 {y}^{3} \\ put \: \: x = y \\ p(y) = {y}^{3} - 2 {y}^{2} .y - 5y. {y}^{2} + 6 {y}^{3} \\ = {y}^{3} - 2 {y}^{3} - 5 {y}^{3} + 6 {y}^{3} \\ = - {y}^{3} + {y}^{3} \\ = 0$

Hence x - y is a factor of polynomial